统计与概率

即时、私密且免费

Combination Calculator.

Calculate n choose k without order or repetition.

设备端计算无需注册

输入数值

输入时结果会更新。

02 / 答案

Combinations

120.000000

Results update automatically as you type.

Use Cases

Probability and Statistics Problems

Quickly find the number of possible combinations for experiments, surveys, or quality control scenarios where order doesn't matter.

Example: Number of ways to choose 3 winners from 10 participants.

Game and Lottery Analysis

Determine the total number of possible outcomes when selecting a subset, such as card hands or lottery numbers.

Example: Possible 5-card poker hands from a 52-card deck.

Frequently Asked Questions

What does the combination calculator compute?: It computes the number of combinations (nCr) of choosing k items from a set of n items, where order does not matter. The formula is n! / (k! * (n-k)!).
What are the valid inputs for n and k?: Both n and k must be non-negative integers. Also, k cannot exceed n. If k > n, the result is zero because you cannot choose more items than available.
Why does the result update instantly?: The calculator uses debounced input handling, meaning it waits briefly after you stop typing before recalculating. This provides immediate feedback without lag, even for large numbers.

Tips & Common Mistakes

Tips

Ensure n and k are non-negative integers; decimals or negative values will not produce valid combinations.
Remember that k must be less than or equal to n. If k > n, the result is zero.
Use the calculator for quick checks of combinatorial identities, like C(n, k) = C(n, n-k).
For large n (e.g., > 1000), results may be extremely large; the calculator handles big integers but may display in scientific notation.

Common Mistakes to Avoid

Entering k greater than n, which yields zero instead of a meaningful count.
Confusing combinations with permutations: combinations ignore order, so C(n, k) is smaller than P(n, k).
Using negative numbers or non-integer values, which are not valid for factorial-based calculations.

Last updated: August 13, 2026

Use Cases

Probability and Statistics Problems

Quickly find the number of possible combinations for experiments, surveys, or quality control scenarios where order doesn't matter.

Example: Number of ways to choose 3 winners from 10 participants.

Game and Lottery Analysis

Determine the total number of possible outcomes when selecting a subset, such as card hands or lottery numbers.

Example: Possible 5-card poker hands from a 52-card deck.

Frequently Asked Questions

What does the combination calculator compute?

It computes the number of combinations (nCr) of choosing k items from a set of n items, where order does not matter. The formula is n! / (k! * (n-k)!).

What are the valid inputs for n and k?

Both n and k must be non-negative integers. Also, k cannot exceed n. If k > n, the result is zero because you cannot choose more items than available.

Why does the result update instantly?

The calculator uses debounced input handling, meaning it waits briefly after you stop typing before recalculating. This provides immediate feedback without lag, even for large numbers.

Tips & Common Mistakes

Tips

Ensure n and k are non-negative integers; decimals or negative values will not produce valid combinations.
Remember that k must be less than or equal to n. If k > n, the result is zero.
Use the calculator for quick checks of combinatorial identities, like C(n, k) = C(n, n-k).
For large n (e.g., > 1000), results may be extremely large; the calculator handles big integers but may display in scientific notation.

Common Mistakes to Avoid

Entering k greater than n, which yields zero instead of a meaningful count.
Confusing combinations with permutations: combinations ignore order, so C(n, k) is smaller than P(n, k).
Using negative numbers or non-integer values, which are not valid for factorial-based calculations.

Use Cases

Probability and Statistics Problems

Quickly find the number of possible combinations for experiments, surveys, or quality control scenarios where order doesn't matter.

Example: Number of ways to choose 3 winners from 10 participants.

Game and Lottery Analysis

Determine the total number of possible outcomes when selecting a subset, such as card hands or lottery numbers.

Example: Possible 5-card poker hands from a 52-card deck.

Frequently Asked Questions

What does the combination calculator compute?

It computes the number of combinations (nCr) of choosing k items from a set of n items, where order does not matter. The formula is n! / (k! * (n-k)!).

What are the valid inputs for n and k?

Both n and k must be non-negative integers. Also, k cannot exceed n. If k > n, the result is zero because you cannot choose more items than available.

Why does the result update instantly?

The calculator uses debounced input handling, meaning it waits briefly after you stop typing before recalculating. This provides immediate feedback without lag, even for large numbers.

Tips & Common Mistakes

Tips

Ensure n and k are non-negative integers; decimals or negative values will not produce valid combinations.
Remember that k must be less than or equal to n. If k > n, the result is zero.
Use the calculator for quick checks of combinatorial identities, like C(n, k) = C(n, n-k).
For large n (e.g., > 1000), results may be extremely large; the calculator handles big integers but may display in scientific notation.

Common Mistakes to Avoid

Entering k greater than n, which yields zero instead of a meaningful count.
Confusing combinations with permutations: combinations ignore order, so C(n, k) is smaller than P(n, k).
Using negative numbers or non-integer values, which are not valid for factorial-based calculations.